Dynamic engineering systems are playing an increasingly important role in society, es- pecially as active and autonomous dynamic systems become more mature and prevalent across a variety of domains. Successful design of complex dynamic systems requires mul- tidisciplinary analysis and design techniques. While multidisciplinary design optimization (MDO) has been used successfully for the development of many dynamic systems, the es- tablished MDO formulations were developed around fundamentally static system models. We still lack general MDO approaches that address the specific needs of dynamic system design. In this article we review the use of MDO for dynamic system design, identify associated challenges, discuss related efforts such as optimal control, and present a vision for fully integrated design approaches. Finally, we lay out a set of exciting new directions that provide an opportunity for fundamental work in MDO.